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2026, Volume 34, Issue 7: 4448-4460. doi: 10.3934/era.2026196
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$ (\sigma, \sigma) $-$ n $-derivations of 3-Lie algebras

  • 1.
    College of Science, Northeast Forestry University, Harbin 150040, China
  • 2.
    College of Materials Science and Engineering, Northeast Forestry University, Harbin 150040, China
  • Published: 25 May 2026

  • In this paper, drawing on the classical theory of skew $ n $-derivations on prime and semiprime rings, we generalize the concept of $ (\sigma, \sigma) $-derivations to the framework of 3-Lie algebras and introduce the notion of $ (\sigma, \sigma) $-$ n $-derivations. Subsequently, several fundamental properties of $ (\sigma, \sigma) $-$ n $-derivations on 3-Lie algebras are established. Furthermore, we prove that the $ (\sigma, \sigma) $-derivation space of any non-abelian 3-dimensional 3-Lie algebra is 6-dimensional, providing a precise dimensional characterization for the low-dimensional case.

    Citation: Rui Zhao, Wenlong Song, Ying Hou. $ (\sigma, \sigma) $-$ n $-derivations of 3-Lie algebras[J]. Electronic Research Archive, 2026, 34(7): 4448-4460. doi: 10.3934/era.2026196

    Related Papers:

  • In this paper, drawing on the classical theory of skew $ n $-derivations on prime and semiprime rings, we generalize the concept of $ (\sigma, \sigma) $-derivations to the framework of 3-Lie algebras and introduce the notion of $ (\sigma, \sigma) $-$ n $-derivations. Subsequently, several fundamental properties of $ (\sigma, \sigma) $-$ n $-derivations on 3-Lie algebras are established. Furthermore, we prove that the $ (\sigma, \sigma) $-derivation space of any non-abelian 3-dimensional 3-Lie algebra is 6-dimensional, providing a precise dimensional characterization for the low-dimensional case.



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